[go: up one dir, main page]

login
A175493
a(n) = Product_{k=1..n} k^d(k), where d(k) = number of divisors of k.
3
1, 4, 36, 2304, 57600, 74649600, 3657830400, 14982473318400, 10922223049113600, 109222230491136000000, 13215889889427456000000, 39462435755592152776704000000, 6669151642695073819262976000000, 256202129505773955840806486016000000
OFFSET
1,2
COMMENTS
a(n) = a(n-1)*A062758(n).
a(n) = Product_{k=1..n} k^floor(n/k) * (floor(n/k))!.
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..117
MATHEMATICA
f[n_] := Product[ k^DivisorSigma[0, k], {k, n}]; Array[f, 15] (* Robert G. Wilson v, Jun 11 2010 *)
PROG
(Python)
from sympy import divisor_count
from itertools import count, islice
def agen():
an = 1
for k in count(2):
yield an
an *= k**divisor_count(k)
print(list(islice(agen(), 14))) # Michael S. Branicky, May 03 2022
(PARI) a(n) = prod(k=1, n, k^numdiv(k)); \\ Michel Marcus, May 03 2022
CROSSREFS
Cf. A062758.
Cf. A174939 (sum instead of product).
Sequence in context: A086857 A174864 A374390 * A179870 A001152 A349848
KEYWORD
nonn
AUTHOR
Leroy Quet, May 30 2010
EXTENSIONS
a(6) onwards from Robert G. Wilson v and Jon E. Schoenfield, Jun 11 2010
a(14) and beyond from Michael S. Branicky, May 03 2022
STATUS
approved